A Bar-Natan homotopy type
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866915535283814400 |
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| author | Sano, Taketo |
| author_facet | Sano, Taketo |
| contents | A spatial refinement of Bar-Natan homology is given, that is, for any link diagram $D$ we construct a CW-spectrum $\mathcal{X}_{\mathit{BN}}(D)$ whose reduced cellular cochain complex gives the Bar-Natan complex of $D$. The stable homotopy type of $\mathcal{X}_{\mathit{BN}}(D)$ is a link invariant and is described as the wedge sum of the canonical cells. We conjecture that the quantum filtration of Bar-Natan homology also lifts to the spatial level, and that it leads us to a cohomotopical refinement of the $s$-invariant. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2102_07529 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A Bar-Natan homotopy type Sano, Taketo Geometric Topology Algebraic Topology 57K18 A spatial refinement of Bar-Natan homology is given, that is, for any link diagram $D$ we construct a CW-spectrum $\mathcal{X}_{\mathit{BN}}(D)$ whose reduced cellular cochain complex gives the Bar-Natan complex of $D$. The stable homotopy type of $\mathcal{X}_{\mathit{BN}}(D)$ is a link invariant and is described as the wedge sum of the canonical cells. We conjecture that the quantum filtration of Bar-Natan homology also lifts to the spatial level, and that it leads us to a cohomotopical refinement of the $s$-invariant. |
| title | A Bar-Natan homotopy type |
| topic | Geometric Topology Algebraic Topology 57K18 |
| url | https://arxiv.org/abs/2102.07529 |